LMFDB - Embedded newform 8017.2.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8017,2,Mod(1,8017)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8017.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0160673005$
Analytic rank:	$0$
Dimension:	$340$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	8017.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.68673 q^{2} +2.91370 q^{3} +5.21852 q^{4} -0.199710 q^{5} -7.82834 q^{6} -2.77102 q^{7} -8.64730 q^{8} +5.48967 q^{9} +O(q^{10})$	\(q-2.68673 q^{2} +2.91370 q^{3} +5.21852 q^{4} -0.199710 q^{5} -7.82834 q^{6} -2.77102 q^{7} -8.64730 q^{8} +5.48967 q^{9} +0.536568 q^{10} -4.81584 q^{11} +15.2052 q^{12} -1.90295 q^{13} +7.44499 q^{14} -0.581897 q^{15} +12.7959 q^{16} +6.61062 q^{17} -14.7493 q^{18} +5.79412 q^{19} -1.04219 q^{20} -8.07394 q^{21} +12.9389 q^{22} -2.00559 q^{23} -25.1957 q^{24} -4.96012 q^{25} +5.11272 q^{26} +7.25417 q^{27} -14.4606 q^{28} +4.08740 q^{29} +1.56340 q^{30} -5.56673 q^{31} -17.0846 q^{32} -14.0319 q^{33} -17.7610 q^{34} +0.553402 q^{35} +28.6480 q^{36} +2.18054 q^{37} -15.5672 q^{38} -5.54464 q^{39} +1.72696 q^{40} -8.02943 q^{41} +21.6925 q^{42} +0.200558 q^{43} -25.1315 q^{44} -1.09635 q^{45} +5.38849 q^{46} +2.76433 q^{47} +37.2835 q^{48} +0.678569 q^{49} +13.3265 q^{50} +19.2614 q^{51} -9.93059 q^{52} +11.7829 q^{53} -19.4900 q^{54} +0.961773 q^{55} +23.9619 q^{56} +16.8824 q^{57} -10.9817 q^{58} +7.01005 q^{59} -3.03664 q^{60} -11.6649 q^{61} +14.9563 q^{62} -15.2120 q^{63} +20.3099 q^{64} +0.380039 q^{65} +37.7000 q^{66} -7.34367 q^{67} +34.4977 q^{68} -5.84370 q^{69} -1.48684 q^{70} +5.75088 q^{71} -47.4708 q^{72} +9.45220 q^{73} -5.85851 q^{74} -14.4523 q^{75} +30.2368 q^{76} +13.3448 q^{77} +14.8969 q^{78} +15.9373 q^{79} -2.55548 q^{80} +4.66748 q^{81} +21.5729 q^{82} -1.02435 q^{83} -42.1340 q^{84} -1.32021 q^{85} -0.538845 q^{86} +11.9095 q^{87} +41.6440 q^{88} -14.4400 q^{89} +2.94558 q^{90} +5.27312 q^{91} -10.4662 q^{92} -16.2198 q^{93} -7.42700 q^{94} -1.15715 q^{95} -49.7794 q^{96} -6.06229 q^{97} -1.82313 q^{98} -26.4374 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9}+O(q^{10}) $ 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9	\( 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9} + 36 q^{10} + 70 q^{11} + 92 q^{12} + 45 q^{13} + 44 q^{14} + 71 q^{15} + 362 q^{16} + 162 q^{17} + 41 q^{18} + 49 q^{19} + 147 q^{20} + 41 q^{21} + 32 q^{22} + 244 q^{23} + 85 q^{24} + 355 q^{25} + 83 q^{26} + 155 q^{27} + 129 q^{28} + 91 q^{29} + 51 q^{30} + 65 q^{31} + 113 q^{32} + 73 q^{33} + 26 q^{34} + 200 q^{35} + 380 q^{36} + 28 q^{37} + 171 q^{38} + 117 q^{39} + 95 q^{40} + 115 q^{41} + 42 q^{42} + 98 q^{43} + 139 q^{44} + 127 q^{45} + 29 q^{46} + 312 q^{47} + 168 q^{48} + 365 q^{49} + 64 q^{50} + 72 q^{51} + 100 q^{52} + 154 q^{53} + 89 q^{54} + 161 q^{55} + 89 q^{56} + 82 q^{57} + 29 q^{58} + 149 q^{59} + 93 q^{60} + 70 q^{61} + 257 q^{62} + 376 q^{63} + 346 q^{64} + 125 q^{65} + 48 q^{66} + 65 q^{67} + 464 q^{68} + 58 q^{69} - 54 q^{70} + 216 q^{71} + 90 q^{72} + 93 q^{73} + 147 q^{74} + 162 q^{75} + 64 q^{76} + 190 q^{77} + 12 q^{78} + 139 q^{79} + 274 q^{80} + 376 q^{81} + 59 q^{82} + 402 q^{83} + 10 q^{84} + 32 q^{85} + 53 q^{86} + 364 q^{87} + 42 q^{88} + 114 q^{89} + 126 q^{90} + 43 q^{91} + 422 q^{92} + 47 q^{93} + 2 q^{94} + 347 q^{95} + 146 q^{96} + 47 q^{97} + 96 q^{98} + 129 q^{99}+O(q^{100}) \) 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9 + 36 * q^10 + 70 * q^11 + 92 * q^12 + 45 * q^13 + 44 * q^14 + 71 * q^15 + 362 * q^16 + 162 * q^17 + 41 * q^18 + 49 * q^19 + 147 * q^20 + 41 * q^21 + 32 * q^22 + 244 * q^23 + 85 * q^24 + 355 * q^25 + 83 * q^26 + 155 * q^27 + 129 * q^28 + 91 * q^29 + 51 * q^30 + 65 * q^31 + 113 * q^32 + 73 * q^33 + 26 * q^34 + 200 * q^35 + 380 * q^36 + 28 * q^37 + 171 * q^38 + 117 * q^39 + 95 * q^40 + 115 * q^41 + 42 * q^42 + 98 * q^43 + 139 * q^44 + 127 * q^45 + 29 * q^46 + 312 * q^47 + 168 * q^48 + 365 * q^49 + 64 * q^50 + 72 * q^51 + 100 * q^52 + 154 * q^53 + 89 * q^54 + 161 * q^55 + 89 * q^56 + 82 * q^57 + 29 * q^58 + 149 * q^59 + 93 * q^60 + 70 * q^61 + 257 * q^62 + 376 * q^63 + 346 * q^64 + 125 * q^65 + 48 * q^66 + 65 * q^67 + 464 * q^68 + 58 * q^69 - 54 * q^70 + 216 * q^71 + 90 * q^72 + 93 * q^73 + 147 * q^74 + 162 * q^75 + 64 * q^76 + 190 * q^77 + 12 * q^78 + 139 * q^79 + 274 * q^80 + 376 * q^81 + 59 * q^82 + 402 * q^83 + 10 * q^84 + 32 * q^85 + 53 * q^86 + 364 * q^87 + 42 * q^88 + 114 * q^89 + 126 * q^90 + 43 * q^91 + 422 * q^92 + 47 * q^93 + 2 * q^94 + 347 * q^95 + 146 * q^96 + 47 * q^97 + 96 * q^98 + 129 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.68673	−1.89981	−0.949903	−	0.312546i	$-0.898818\pi$
$2$	−2.68673	−1.89981	−0.949903	+	0.312546i	$0.898818\pi$
$3$	2.91370	1.68223	0.841114	−	0.540858i	$-0.181900\pi$
$3$	2.91370	1.68223	0.841114	+	0.540858i	$0.181900\pi$
$4$	5.21852	2.60926
$5$	−0.199710	−0.0893132	−0.0446566	−	0.999002i	$-0.514219\pi$
$5$	−0.199710	−0.0893132	−0.0446566	+	0.999002i	$0.514219\pi$
$6$	−7.82834	−3.19591
$7$	−2.77102	−1.04735	−0.523674	−	0.851919i	$-0.675439\pi$
$7$	−2.77102	−1.04735	−0.523674	+	0.851919i	$0.675439\pi$
$8$	−8.64730	−3.05728
$9$	5.48967	1.82989
$10$	0.536568	0.169678
$11$	−4.81584	−1.45203	−0.726015	−	0.687679i	$-0.758630\pi$
$11$	−4.81584	−1.45203	−0.726015	+	0.687679i	$0.758630\pi$
$12$	15.2052	4.38937
$13$	−1.90295	−0.527784	−0.263892	−	0.964552i	$-0.585006\pi$
$13$	−1.90295	−0.527784	−0.263892	+	0.964552i	$0.585006\pi$
$14$	7.44499	1.98976
$15$	−0.581897	−0.150245
$16$	12.7959	3.19898
$17$	6.61062	1.60331	0.801656	−	0.597786i	$-0.203953\pi$
$17$	6.61062	1.60331	0.801656	+	0.597786i	$0.203953\pi$
$18$	−14.7493	−3.47644
$19$	5.79412	1.32926	0.664631	−	0.747171i	$-0.268589\pi$
$19$	5.79412	1.32926	0.664631	+	0.747171i	$0.268589\pi$
$20$	−1.04219	−0.233042
$21$	−8.07394	−1.76188
$22$	12.9389	2.75857
$23$	−2.00559	−0.418195	−0.209097	−	0.977895i	$-0.567053\pi$
$23$	−2.00559	−0.418195	−0.209097	+	0.977895i	$0.567053\pi$
$24$	−25.1957	−5.14304
$25$	−4.96012	−0.992023
$26$	5.11272	1.00269
$27$	7.25417	1.39607
$28$	−14.4606	−2.73280
$29$	4.08740	0.759010	0.379505	−	0.925190i	$-0.376094\pi$
$29$	4.08740	0.759010	0.379505	+	0.925190i	$0.376094\pi$
$30$	1.56340	0.285437
$31$	−5.56673	−0.999814	−0.499907	−	0.866079i	$-0.666633\pi$
$31$	−5.56673	−0.999814	−0.499907	+	0.866079i	$0.666633\pi$
$32$	−17.0846	−3.02016
$33$	−14.0319	−2.44264
$34$	−17.7610	−3.04598
$35$	0.553402	0.0935421
$36$	28.6480	4.77466
$37$	2.18054	0.358478	0.179239	−	0.983806i	$-0.442636\pi$
$37$	2.18054	0.358478	0.179239	+	0.983806i	$0.442636\pi$
$38$	−15.5672	−2.52534
$39$	−5.54464	−0.887852
$40$	1.72696	0.273056
$41$	−8.02943	−1.25399	−0.626993	−	0.779025i	$-0.715714\pi$
$41$	−8.02943	−1.25399	−0.626993	+	0.779025i	$0.715714\pi$
$42$	21.6925	3.34723
$43$	0.200558	0.0305848	0.0152924	−	0.999883i	$-0.495132\pi$
$43$	0.200558	0.0305848	0.0152924	+	0.999883i	$0.495132\pi$
$44$	−25.1315	−3.78872
$45$	−1.09635	−0.163433
$46$	5.38849	0.794489
$47$	2.76433	0.403218	0.201609	−	0.979466i	$-0.435383\pi$
$47$	2.76433	0.403218	0.201609	+	0.979466i	$0.435383\pi$
$48$	37.2835	5.38141
$49$	0.678569	0.0969384
$50$	13.3265	1.88465
$51$	19.2614	2.69714
$52$	−9.93059	−1.37712
$53$	11.7829	1.61850	0.809252	−	0.587462i	$-0.199873\pi$
$53$	11.7829	1.61850	0.809252	+	0.587462i	$0.199873\pi$
$54$	−19.4900	−2.65225
$55$	0.961773	0.129685
$56$	23.9619	3.20204
$57$	16.8824	2.23612
$58$	−10.9817	−1.44197
$59$	7.01005	0.912631	0.456315	−	0.889818i	$-0.349169\pi$
$59$	7.01005	0.912631	0.456315	+	0.889818i	$0.349169\pi$
$60$	−3.03664	−0.392029
$61$	−11.6649	−1.49353	−0.746766	−	0.665087i	$-0.768395\pi$
$61$	−11.6649	−1.49353	−0.746766	+	0.665087i	$0.768395\pi$
$62$	14.9563	1.89945
$63$	−15.2120	−1.91653
$64$	20.3099	2.53873
$65$	0.380039	0.0471381
$66$	37.7000	4.64055
$67$	−7.34367	−0.897171	−0.448586	−	0.893740i	$-0.648072\pi$
$67$	−7.34367	−0.897171	−0.448586	+	0.893740i	$0.648072\pi$
$68$	34.4977	4.18346
$69$	−5.84370	−0.703499
$70$	−1.48684	−0.177712
$71$	5.75088	0.682504	0.341252	−	0.939972i	$-0.389149\pi$
$71$	5.75088	0.682504	0.341252	+	0.939972i	$0.389149\pi$
$72$	−47.4708	−5.59449
$73$	9.45220	1.10630	0.553148	−	0.833083i	$-0.313426\pi$
$73$	9.45220	1.10630	0.553148	+	0.833083i	$0.313426\pi$
$74$	−5.85851	−0.681039
$75$	−14.4523	−1.66881
$76$	30.2368	3.46839
$77$	13.3448	1.52078
$78$	14.8969	1.68675
$79$	15.9373	1.79309	0.896544	−	0.442954i	$-0.146069\pi$
$79$	15.9373	1.79309	0.896544	+	0.442954i	$0.146069\pi$
$80$	−2.55548	−0.285711
$81$	4.66748	0.518609
$82$	21.5729	2.38233
$83$	−1.02435	−0.112437	−0.0562187	−	0.998418i	$-0.517904\pi$
$83$	−1.02435	−0.112437	−0.0562187	+	0.998418i	$0.517904\pi$
$84$	−42.1340	−4.59720
$85$	−1.32021	−0.143197
$86$	−0.538845	−0.0581052
$87$	11.9095	1.27683
$88$	41.6440	4.43926
$89$	−14.4400	−1.53063	−0.765317	−	0.643654i	$-0.777418\pi$
$89$	−14.4400	−1.53063	−0.765317	+	0.643654i	$0.777418\pi$
$90$	2.94558	0.310492
$91$	5.27312	0.552773
$92$	−10.4662	−1.09118
$93$	−16.2198	−1.68192
$94$	−7.42700	−0.766036
$95$	−1.15715	−0.118721
$96$	−49.7794	−5.08059
$97$	−6.06229	−0.615532	−0.307766	−	0.951462i	$-0.599581\pi$
$97$	−6.06229	−0.615532	−0.307766	+	0.951462i	$0.599581\pi$
$98$	−1.82313	−0.184164
$99$	−26.4374	−2.65705
$100$	−25.8845	−2.58845
$101$	16.4626	1.63809	0.819047	−	0.573727i	$-0.194503\pi$
$101$	16.4626	1.63809	0.819047	+	0.573727i	$0.194503\pi$
$102$	−51.7502	−5.12403
$103$	−5.47008	−0.538983	−0.269491	−	0.963003i	$-0.586856\pi$
$103$	−5.47008	−0.538983	−0.269491	+	0.963003i	$0.586856\pi$
$104$	16.4554	1.61358
$105$	1.61245	0.157359
$106$	−31.6574	−3.07484
$107$	18.4028	1.77907	0.889533	−	0.456871i	$-0.151030\pi$
$107$	18.4028	1.77907	0.889533	+	0.456871i	$0.151030\pi$
$108$	37.8560	3.64270
$109$	18.0846	1.73219	0.866097	−	0.499876i	$-0.166621\pi$
$109$	18.0846	1.73219	0.866097	+	0.499876i	$0.166621\pi$
$110$	−2.58402	−0.246377
$111$	6.35344	0.603042
$112$	−35.4578	−3.35045
$113$	2.40567	0.226306	0.113153	−	0.993578i	$-0.463905\pi$
$113$	2.40567	0.226306	0.113153	+	0.993578i	$0.463905\pi$
$114$	−45.3584	−4.24820
$115$	0.400538	0.0373503
$116$	21.3302	1.98046
$117$	−10.4466	−0.965786
$118$	−18.8341	−1.73382
$119$	−18.3182	−1.67923
$120$	5.03184	0.459342
$121$	12.1923	1.10839
$122$	31.3403	2.83742
$123$	−23.3954	−2.10949
$124$	−29.0501	−2.60878
$125$	1.98914	0.177914
$126$	40.8706	3.64104
$127$	−9.73392	−0.863745	−0.431873	−	0.901935i	$-0.642147\pi$
$127$	−9.73392	−0.863745	−0.431873	+	0.901935i	$0.642147\pi$
$128$	−20.3979	−1.80294
$129$	0.584367	0.0514506
$130$	−1.02106	−0.0895531
$131$	9.15377	0.799769	0.399884	−	0.916566i	$-0.369050\pi$
$131$	9.15377	0.799769	0.399884	+	0.916566i	$0.369050\pi$
$132$	−73.2259	−6.37350
$133$	−16.0556	−1.39220
$134$	19.7304	1.70445
$135$	−1.44873	−0.124687
$136$	−57.1640	−4.90178
$137$	2.19448	0.187487	0.0937436	−	0.995596i	$-0.470117\pi$
$137$	2.19448	0.187487	0.0937436	+	0.995596i	$0.470117\pi$
$138$	15.7005	1.33651
$139$	−11.6912	−0.991632	−0.495816	−	0.868427i	$-0.665131\pi$
$139$	−11.6912	−0.991632	−0.495816	+	0.868427i	$0.665131\pi$
$140$	2.88794	0.244076
$141$	8.05443	0.678305
$142$	−15.4511	−1.29662
$143$	9.16430	0.766357
$144$	70.2454	5.85378
$145$	−0.816296	−0.0677897
$146$	−25.3955	−2.10175
$147$	1.97715	0.163073
$148$	11.3792	0.935363
$149$	0.873354	0.0715479	0.0357740	−	0.999360i	$-0.488610\pi$
$149$	0.873354	0.0715479	0.0357740	+	0.999360i	$0.488610\pi$
$150$	38.8295	3.17041
$151$	23.4116	1.90521	0.952605	−	0.304211i	$-0.0983929\pi$
$151$	23.4116	1.90521	0.952605	+	0.304211i	$0.0983929\pi$
$152$	−50.1035	−4.06393
$153$	36.2902	2.93389
$154$	−35.8539	−2.88919
$155$	1.11173	0.0892966
$156$	−28.9348	−2.31664
$157$	−23.5461	−1.87918	−0.939592	−	0.342297i	$-0.888795\pi$
$157$	−23.5461	−1.87918	−0.939592	+	0.342297i	$0.888795\pi$
$158$	−42.8193	−3.40652
$159$	34.3319	2.72269
$160$	3.41197	0.269740
$161$	5.55754	0.437996
$162$	−12.5403	−0.985257
$163$	0.0316096	0.00247585	0.00123793	−	0.999999i	$-0.499606\pi$
$163$	0.0316096	0.00247585	0.00123793	+	0.999999i	$0.499606\pi$
$164$	−41.9017	−3.27197
$165$	2.80232	0.218160
$166$	2.75216	0.213609
$167$	2.37298	0.183626	0.0918132	−	0.995776i	$-0.470734\pi$
$167$	2.37298	0.183626	0.0918132	+	0.995776i	$0.470734\pi$
$168$	69.8178	5.38656
$169$	−9.37878	−0.721444
$170$	3.54705	0.272046
$171$	31.8078	2.43241
$172$	1.04662	0.0798037
$173$	10.1292	0.770105	0.385053	−	0.922895i	$-0.374183\pi$
$173$	10.1292	0.770105	0.385053	+	0.922895i	$0.374183\pi$
$174$	−31.9975	−2.42573
$175$	13.7446	1.03899
$176$	−61.6231	−4.64501
$177$	20.4252	1.53525
$178$	38.7963	2.90791
$179$	5.88447	0.439826	0.219913	−	0.975519i	$-0.429423\pi$
$179$	5.88447	0.439826	0.219913	+	0.975519i	$0.429423\pi$
$180$	−5.72130	−0.426440
$181$	18.8575	1.40166	0.700832	−	0.713326i	$-0.252812\pi$
$181$	18.8575	1.40166	0.700832	+	0.713326i	$0.252812\pi$
$182$	−14.1675	−1.05016
$183$	−33.9879	−2.51246
$184$	17.3430	1.27854
$185$	−0.435476	−0.0320168
$186$	43.5782	3.19531
$187$	−31.8357	−2.32806
$188$	14.4257	1.05210
$189$	−20.1015	−1.46217
$190$	3.10894	0.225546
$191$	14.0846	1.01913	0.509563	−	0.860433i	$-0.329807\pi$
$191$	14.0846	1.01913	0.509563	+	0.860433i	$0.329807\pi$
$192$	59.1769	4.27072
$193$	0.183801	0.0132303	0.00661514	−	0.999978i	$-0.497894\pi$
$193$	0.183801	0.0132303	0.00661514	+	0.999978i	$0.497894\pi$
$194$	16.2877	1.16939
$195$	1.10732	0.0792970
$196$	3.54113	0.252938
$197$	−13.2979	−0.947434	−0.473717	−	0.880677i	$-0.657088\pi$
$197$	−13.2979	−0.947434	−0.473717	+	0.880677i	$0.657088\pi$
$198$	71.0301	5.04789
$199$	6.85092	0.485649	0.242825	−	0.970070i	$-0.421926\pi$
$199$	6.85092	0.485649	0.242825	+	0.970070i	$0.421926\pi$
$200$	42.8916	3.03289
$201$	−21.3973	−1.50925
$202$	−44.2307	−3.11206
$203$	−11.3263	−0.794948
$204$	100.516	7.03753
$205$	1.60356	0.111998
$206$	14.6966	1.02396
$207$	−11.0100	−0.765251
$208$	−24.3500	−1.68837
$209$	−27.9035	−1.93013
$210$	−4.33222	−0.298952
$211$	−18.8670	−1.29886	−0.649429	−	0.760423i	$-0.724992\pi$
$211$	−18.8670	−1.29886	−0.649429	+	0.760423i	$0.724992\pi$
$212$	61.4893	4.22310
$213$	16.7564	1.14813
$214$	−49.4434	−3.37988
$215$	−0.0400535	−0.00273163
$216$	−62.7290	−4.26817
$217$	15.4255	1.04715
$218$	−48.5885	−3.29083
$219$	27.5409	1.86104
$220$	5.01903	0.338383
$221$	−12.5797	−0.846202
$222$	−17.0700	−1.14566
$223$	20.0819	1.34478	0.672390	−	0.740197i	$-0.265268\pi$
$223$	20.0819	1.34478	0.672390	+	0.740197i	$0.265268\pi$
$224$	47.3418	3.16316
$225$	−27.2294	−1.81529
$226$	−6.46339	−0.429938
$227$	−14.3132	−0.949998	−0.474999	−	0.879986i	$-0.657552\pi$
$227$	−14.3132	−0.949998	−0.474999	+	0.879986i	$0.657552\pi$
$228$	88.1010	5.83463
$229$	−18.7017	−1.23584	−0.617922	−	0.786239i	$-0.712025\pi$
$229$	−18.7017	−1.23584	−0.617922	+	0.786239i	$0.712025\pi$
$230$	−1.07614	−0.0709584
$231$	38.8828	2.55830
$232$	−35.3449	−2.32051
$233$	2.53364	0.165984	0.0829920	−	0.996550i	$-0.473552\pi$
$233$	2.53364	0.165984	0.0829920	+	0.996550i	$0.473552\pi$
$234$	28.0671	1.83481
$235$	−0.552065	−0.0360127
$236$	36.5821	2.38129
$237$	46.4366	3.01638
$238$	49.2160	3.19020
$239$	3.17183	0.205168	0.102584	−	0.994724i	$-0.467289\pi$
$239$	3.17183	0.205168	0.102584	+	0.994724i	$0.467289\pi$
$240$	−7.44591	−0.480631
$241$	27.9573	1.80089	0.900444	−	0.434972i	$-0.143242\pi$
$241$	27.9573	1.80089	0.900444	+	0.434972i	$0.143242\pi$
$242$	−32.7574	−2.10572
$243$	−8.16284	−0.523646
$244$	−60.8733	−3.89701
$245$	−0.135517	−0.00865788
$246$	62.8571	4.00762
$247$	−11.0259	−0.701563
$248$	48.1372	3.05671
$249$	−2.98466	−0.189145
$250$	−5.34428	−0.338002
$251$	−14.8975	−0.940323	−0.470161	−	0.882580i	$-0.655804\pi$
$251$	−14.8975	−0.940323	−0.470161	+	0.882580i	$0.655804\pi$
$252$	−79.3842	−5.00073
$253$	9.65860	0.607231
$254$	26.1524	1.64095
$255$	−3.84670	−0.240890
$256$	14.1840	0.886500
$257$	27.9319	1.74235	0.871174	−	0.490975i	$-0.163359\pi$
$257$	27.9319	1.74235	0.871174	+	0.490975i	$0.163359\pi$
$258$	−1.57004	−0.0977461
$259$	−6.04232	−0.375451
$260$	1.98324	0.122995
$261$	22.4385	1.38891
$262$	−24.5937	−1.51941
$263$	−5.25921	−0.324297	−0.162148	−	0.986766i	$-0.551842\pi$
$263$	−5.25921	−0.324297	−0.162148	+	0.986766i	$0.551842\pi$
$264$	121.338	7.46785
$265$	−2.35317	−0.144554
$266$	43.1372	2.64491
$267$	−42.0738	−2.57487
$268$	−38.3231	−2.34095
$269$	0.636040	0.0387800	0.0193900	−	0.999812i	$-0.493828\pi$
$269$	0.636040	0.0387800	0.0193900	+	0.999812i	$0.493828\pi$
$270$	3.89236	0.236881
$271$	−0.985574	−0.0598694	−0.0299347	−	0.999552i	$-0.509530\pi$
$271$	−0.985574	−0.0598694	−0.0299347	+	0.999552i	$0.509530\pi$
$272$	84.5890	5.12896
$273$	15.3643	0.929891
$274$	−5.89598	−0.356189
$275$	23.8871	1.44045
$276$	−30.4955	−1.83561
$277$	19.6070	1.17807	0.589037	−	0.808106i	$-0.299507\pi$
$277$	19.6070	1.17807	0.589037	+	0.808106i	$0.299507\pi$
$278$	31.4110	1.88391
$279$	−30.5595	−1.82955
$280$	−4.78544	−0.285984
$281$	−6.20651	−0.370249	−0.185125	−	0.982715i	$-0.559269\pi$
$281$	−6.20651	−0.370249	−0.185125	+	0.982715i	$0.559269\pi$
$282$	−21.6401	−1.28865
$283$	20.9060	1.24273	0.621366	−	0.783521i	$-0.286578\pi$
$283$	20.9060	1.24273	0.621366	+	0.783521i	$0.286578\pi$
$284$	30.0111	1.78083
$285$	−3.37158	−0.199715
$286$	−24.6220	−1.45593
$287$	22.2497	1.31336
$288$	−93.7888	−5.52656
$289$	26.7003	1.57061
$290$	2.19317	0.128787
$291$	−17.6637	−1.03547
$292$	49.3265	2.88662
$293$	30.4569	1.77931	0.889656	−	0.456631i	$-0.150944\pi$
$293$	30.4569	1.77931	0.889656	+	0.456631i	$0.150944\pi$
$294$	−5.31207	−0.309806
$295$	−1.39998	−0.0815100
$296$	−18.8558	−1.09597
$297$	−34.9349	−2.02713
$298$	−2.34647	−0.135927
$299$	3.81654	0.220716
$300$	−75.4197	−4.35436
$301$	−0.555751	−0.0320329
$302$	−62.9007	−3.61953
$303$	47.9672	2.75565
$304$	74.1411	4.25229
$305$	2.32959	0.133392
$306$	−97.5019	−5.57381
$307$	9.74852	0.556377	0.278189	−	0.960526i	$-0.410266\pi$
$307$	9.74852	0.556377	0.278189	+	0.960526i	$0.410266\pi$
$308$	69.6401	3.96811
$309$	−15.9382	−0.906692
$310$	−2.98693	−0.169646
$311$	19.7286	1.11870	0.559352	−	0.828930i	$-0.311050\pi$
$311$	19.7286	1.11870	0.559352	+	0.828930i	$0.311050\pi$
$312$	47.9461	2.71441
$313$	1.25589	0.0709871	0.0354936	−	0.999370i	$-0.488700\pi$
$313$	1.25589	0.0709871	0.0354936	+	0.999370i	$0.488700\pi$
$314$	63.2620	3.57008
$315$	3.03800	0.171172
$316$	83.1693	4.67864
$317$	18.4465	1.03606	0.518028	−	0.855364i	$-0.326666\pi$
$317$	18.4465	1.03606	0.518028	+	0.855364i	$0.326666\pi$
$318$	−92.2404	−5.17259
$319$	−19.6842	−1.10211
$320$	−4.05609	−0.226742
$321$	53.6203	2.99279
$322$	−14.9316	−0.832107
$323$	38.3028	2.13122
$324$	24.3574	1.35319
$325$	9.43886	0.523574
$326$	−0.0849264	−0.00470364
$327$	52.6933	2.91394
$328$	69.4328	3.83379
$329$	−7.66001	−0.422310
$330$	−7.52908	−0.414462
$331$	31.9918	1.75843	0.879213	−	0.476429i	$-0.158069\pi$
$331$	31.9918	1.75843	0.879213	+	0.476429i	$0.158069\pi$
$332$	−5.34561	−0.293379
$333$	11.9704	0.655976
$334$	−6.37555	−0.348854
$335$	1.46661	0.0801293
$336$	−103.314	−5.63621
$337$	−18.8653	−1.02766	−0.513829	−	0.857892i	$-0.671774\pi$
$337$	−18.8653	−1.02766	−0.513829	+	0.857892i	$0.671774\pi$
$338$	25.1982	1.37060
$339$	7.00941	0.380699
$340$	−6.88955	−0.373638
$341$	26.8085	1.45176
$342$	−85.4591	−4.62110
$343$	17.5168	0.945820
$344$	−1.73428	−0.0935064
$345$	1.16705	0.0628318
$346$	−27.2143	−1.46305
$347$	0.224535	0.0120537	0.00602685	−	0.999982i	$-0.498082\pi$
$347$	0.224535	0.0120537	0.00602685	+	0.999982i	$0.498082\pi$
$348$	62.1498	3.33158
$349$	−12.7563	−0.682831	−0.341415	−	0.939913i	$-0.610906\pi$
$349$	−12.7563	−0.682831	−0.341415	+	0.939913i	$0.610906\pi$
$350$	−36.9280	−1.97389
$351$	−13.8043	−0.736820
$352$	82.2766	4.38536
$353$	20.8629	1.11042	0.555210	−	0.831710i	$-0.312638\pi$
$353$	20.8629	1.11042	0.555210	+	0.831710i	$0.312638\pi$
$354$	−54.8770	−2.91668
$355$	−1.14851	−0.0609566
$356$	−75.3553	−3.99382
$357$	−53.3738	−2.82484
$358$	−15.8100	−0.835584
$359$	10.0579	0.530837	0.265419	−	0.964133i	$-0.414490\pi$
$359$	10.0579	0.530837	0.265419	+	0.964133i	$0.414490\pi$
$360$	9.48042	0.499662
$361$	14.5719	0.766940
$362$	−50.6649	−2.66289
$363$	35.5247	1.86456
$364$	27.5179	1.44233
$365$	−1.88770	−0.0988069
$366$	91.3165	4.77319
$367$	−6.78299	−0.354069	−0.177035	−	0.984205i	$-0.556650\pi$
$367$	−6.78299	−0.354069	−0.177035	+	0.984205i	$0.556650\pi$
$368$	−25.6634	−1.33780
$369$	−44.0789	−2.29466
$370$	1.17001	0.0608258
$371$	−32.6507	−1.69514
$372$	−84.6434	−4.38856
$373$	9.69114	0.501788	0.250894	−	0.968015i	$-0.419275\pi$
$373$	9.69114	0.501788	0.250894	+	0.968015i	$0.419275\pi$
$374$	85.5339	4.42285
$375$	5.79576	0.299292
$376$	−23.9039	−1.23275
$377$	−7.77811	−0.400593
$378$	54.0072	2.77783
$379$	−30.2975	−1.55628	−0.778138	−	0.628093i	$-0.783836\pi$
$379$	−30.2975	−1.55628	−0.778138	+	0.628093i	$0.783836\pi$
$380$	−6.03860	−0.309773
$381$	−28.3618	−1.45302
$382$	−37.8415	−1.93614
$383$	15.1098	0.772074	0.386037	−	0.922483i	$-0.373844\pi$
$383$	15.1098	0.772074	0.386037	+	0.922483i	$0.373844\pi$
$384$	−59.4335	−3.03295
$385$	−2.66510	−0.135826
$386$	−0.493824	−0.0251350
$387$	1.10100	0.0559668
$388$	−31.6362	−1.60608
$389$	11.7984	0.598201	0.299101	−	0.954222i	$-0.403313\pi$
$389$	11.7984	0.598201	0.299101	+	0.954222i	$0.403313\pi$
$390$	−2.97508	−0.150649
$391$	−13.2582	−0.670497
$392$	−5.86779	−0.296368
$393$	26.6714	1.34539
$394$	35.7278	1.79994
$395$	−3.18285	−0.160147
$396$	−137.964	−6.93295
$397$	−0.183537	−0.00921144	−0.00460572	−	0.999989i	$-0.501466\pi$
$397$	−0.183537	−0.00921144	−0.00460572	+	0.999989i	$0.501466\pi$
$398$	−18.4066	−0.922639
$399$	−46.7814	−2.34200
$400$	−63.4692	−3.17346
$401$	−15.1970	−0.758904	−0.379452	−	0.925211i	$-0.623887\pi$
$401$	−15.1970	−0.758904	−0.379452	+	0.925211i	$0.623887\pi$
$402$	57.4887	2.86728
$403$	10.5932	0.527686
$404$	85.9106	4.27421
$405$	−0.932145	−0.0463187
$406$	30.4306	1.51025
$407$	−10.5011	−0.520521
$408$	−166.559	−8.24590
$409$	−15.5327	−0.768042	−0.384021	−	0.923324i	$-0.625461\pi$
$409$	−15.5327	−0.768042	−0.384021	+	0.923324i	$0.625461\pi$
$410$	−4.30833	−0.212773
$411$	6.39407	0.315396
$412$	−28.5457	−1.40635
$413$	−19.4250	−0.955842
$414$	29.5810	1.45383
$415$	0.204574	0.0100422
$416$	32.5111	1.59399
$417$	−34.0646	−1.66815
$418$	74.9693	3.66687
$419$	12.4757	0.609480	0.304740	−	0.952436i	$-0.401431\pi$
$419$	12.4757	0.609480	0.304740	+	0.952436i	$0.401431\pi$
$420$	8.41461	0.410591
$421$	7.33518	0.357495	0.178747	−	0.983895i	$-0.442796\pi$
$421$	7.33518	0.357495	0.178747	+	0.983895i	$0.442796\pi$
$422$	50.6905	2.46758
$423$	15.1752	0.737845
$424$	−101.890	−4.94822
$425$	−32.7895	−1.59052
$426$	−45.0198	−2.18122
$427$	32.3236	1.56425
$428$	96.0354	4.64205
$429$	26.7021	1.28919
$430$	0.107613	0.00518956
$431$	10.6689	0.513901	0.256951	−	0.966425i	$-0.417282\pi$
$431$	10.6689	0.513901	0.256951	+	0.966425i	$0.417282\pi$
$432$	92.8238	4.46598
$433$	−30.8329	−1.48174	−0.740868	−	0.671651i	$-0.765586\pi$
$433$	−30.8329	−1.48174	−0.740868	+	0.671651i	$0.765586\pi$
$434$	−41.4443	−1.98939
$435$	−2.37844	−0.114038
$436$	94.3750	4.51974
$437$	−11.6206	−0.555891
$438$	−73.9950	−3.53562
$439$	−34.3219	−1.63810	−0.819048	−	0.573724i	$-0.805498\pi$
$439$	−34.3219	−1.63810	−0.819048	+	0.573724i	$0.805498\pi$
$440$	−8.31674	−0.396485
$441$	3.72512	0.177387
$442$	33.7982	1.60762
$443$	−15.9904	−0.759729	−0.379864	−	0.925042i	$-0.624029\pi$
$443$	−15.9904	−0.759729	−0.379864	+	0.925042i	$0.624029\pi$
$444$	33.1556	1.57349
$445$	2.88381	0.136706
$446$	−53.9545	−2.55482
$447$	2.54469	0.120360
$448$	−56.2791	−2.65894
$449$	−4.79247	−0.226170	−0.113085	−	0.993585i	$-0.536073\pi$
$449$	−4.79247	−0.226170	−0.113085	+	0.993585i	$0.536073\pi$
$450$	73.1581	3.44871
$451$	38.6684	1.82082
$452$	12.5540	0.590492
$453$	68.2145	3.20500
$454$	38.4556	1.80481
$455$	−1.05310	−0.0493700
$456$	−145.987	−6.83646
$457$	36.1670	1.69182	0.845910	−	0.533326i	$-0.179058\pi$
$457$	36.1670	1.69182	0.845910	+	0.533326i	$0.179058\pi$
$458$	50.2465	2.34786
$459$	47.9546	2.23833
$460$	2.09021	0.0974568
$461$	−40.8009	−1.90029	−0.950144	−	0.311811i	$-0.899064\pi$
$461$	−40.8009	−1.90029	−0.950144	+	0.311811i	$0.899064\pi$
$462$	−104.468	−4.86027
$463$	14.7090	0.683586	0.341793	−	0.939775i	$-0.388966\pi$
$463$	14.7090	0.683586	0.341793	+	0.939775i	$0.388966\pi$
$464$	52.3020	2.42806
$465$	3.23926	0.150217
$466$	−6.80720	−0.315337
$467$	−41.1557	−1.90446	−0.952229	−	0.305386i	$-0.901215\pi$
$467$	−41.1557	−1.90446	−0.952229	+	0.305386i	$0.901215\pi$
$468$	−54.5157	−2.51999
$469$	20.3495	0.939651
$470$	1.48325	0.0684172
$471$	−68.6064	−3.16122
$472$	−60.6180	−2.79017
$473$	−0.965854	−0.0444100
$474$	−124.763	−5.73054
$475$	−28.7395	−1.31866
$476$	−95.5939	−4.38154
$477$	64.6842	2.96169
$478$	−8.52184	−0.389780
$479$	−6.02647	−0.275357	−0.137678	−	0.990477i	$-0.543964\pi$
$479$	−6.02647	−0.275357	−0.137678	+	0.990477i	$0.543964\pi$
$480$	9.94148	0.453764
$481$	−4.14945	−0.189199
$482$	−75.1137	−3.42134
$483$	16.1930	0.736809
$484$	63.6257	2.89208
$485$	1.21070	0.0549752
$486$	21.9313	0.994826
$487$	22.1806	1.00510	0.502549	−	0.864549i	$-0.332396\pi$
$487$	22.1806	1.00510	0.502549	+	0.864549i	$0.332396\pi$
$488$	100.870	4.56615
$489$	0.0921010	0.00416495
$490$	0.364099	0.0164483
$491$	−2.50629	−0.113107	−0.0565537	−	0.998400i	$-0.518011\pi$
$491$	−2.50629	−0.113107	−0.0565537	+	0.998400i	$0.518011\pi$
$492$	−122.089	−5.50421
$493$	27.0202	1.21693
$494$	29.6237	1.33283
$495$	5.27982	0.237310
$496$	−71.2314	−3.19839
$497$	−15.9358	−0.714819
$498$	8.01899	0.359340
$499$	−0.711737	−0.0318617	−0.0159309	−	0.999873i	$-0.505071\pi$
$499$	−0.711737	−0.0318617	−0.0159309	+	0.999873i	$0.505071\pi$
$500$	10.3804	0.464224
$501$	6.91415	0.308901
$502$	40.0256	1.78643
$503$	−1.93191	−0.0861397	−0.0430698	−	0.999072i	$-0.513714\pi$
$503$	−1.93191	−0.0861397	−0.0430698	+	0.999072i	$0.513714\pi$
$504$	131.543	5.85938
$505$	−3.28776	−0.146303
$506$	−25.9501	−1.15362
$507$	−27.3270	−1.21363
$508$	−50.7966	−2.25374
$509$	18.7732	0.832109	0.416055	−	0.909340i	$-0.363412\pi$
$509$	18.7732	0.832109	0.416055	+	0.909340i	$0.363412\pi$
$510$	10.3351	0.457644
$511$	−26.1923	−1.15868
$512$	2.68724	0.118760
$513$	42.0315	1.85574
$514$	−75.0456	−3.31012
$515$	1.09243	0.0481383
$516$	3.04953	0.134248
$517$	−13.3125	−0.585485
$518$	16.2341	0.713285
$519$	29.5134	1.29549
$520$	−3.28631	−0.144114
$521$	33.3951	1.46306	0.731532	−	0.681807i	$-0.238806\pi$
$521$	33.3951	1.46306	0.731532	+	0.681807i	$0.238806\pi$
$522$	−60.2861	−2.63865
$523$	41.2918	1.80556	0.902782	−	0.430099i	$-0.141521\pi$
$523$	41.2918	1.80556	0.902782	+	0.430099i	$0.141521\pi$
$524$	47.7692	2.08681
$525$	40.0477	1.74782
$526$	14.1301	0.616101
$527$	−36.7996	−1.60301
$528$	−179.551	−7.81397
$529$	−18.9776	−0.825113
$530$	6.32232	0.274624
$531$	38.4829	1.67001
$532$	−83.7867	−3.63262
$533$	15.2796	0.661833
$534$	113.041	4.89176
$535$	−3.67523	−0.158894
$536$	63.5029	2.74291
$537$	17.1456	0.739887
$538$	−1.70887	−0.0736745
$539$	−3.26788	−0.140757
$540$	−7.56025	−0.325341
$541$	−39.6317	−1.70390	−0.851951	−	0.523622i	$-0.824581\pi$
$541$	−39.6317	−1.70390	−0.851951	+	0.523622i	$0.824581\pi$
$542$	2.64797	0.113740
$543$	54.9451	2.35792
$544$	−112.940	−4.84225
$545$	−3.61169	−0.154708
$546$	−41.2798	−1.76661
$547$	45.8275	1.95944	0.979721	−	0.200364i	$-0.0642126\pi$
$547$	45.8275	1.95944	0.979721	+	0.200364i	$0.0642126\pi$
$548$	11.4519	0.489203
$549$	−64.0362	−2.73300
$550$	−64.1782	−2.73657
$551$	23.6829	1.00892
$552$	50.5322	2.15079
$553$	−44.1627	−1.87799
$554$	−52.6788	−2.23811
$555$	−1.26885	−0.0538596
$556$	−61.0106	−2.58743
$557$	35.7048	1.51286	0.756431	−	0.654074i	$-0.226941\pi$
$557$	35.7048	1.51286	0.756431	+	0.654074i	$0.226941\pi$
$558$	82.1052	3.47579
$559$	−0.381652	−0.0161422
$560$	7.08129	0.299239
$561$	−92.7598	−3.91632
$562$	16.6752	0.703402
$563$	10.1486	0.427714	0.213857	−	0.976865i	$-0.431397\pi$
$563$	10.1486	0.427714	0.213857	+	0.976865i	$0.431397\pi$
$564$	42.0322	1.76987
$565$	−0.480437	−0.0202122
$566$	−56.1687	−2.36095
$567$	−12.9337	−0.543165
$568$	−49.7295	−2.08661
$569$	8.37669	0.351169	0.175584	−	0.984464i	$-0.443818\pi$
$569$	8.37669	0.351169	0.175584	+	0.984464i	$0.443818\pi$
$570$	9.05854	0.379420
$571$	−29.1624	−1.22041	−0.610203	−	0.792245i	$-0.708912\pi$
$571$	−29.1624	−1.22041	−0.610203	+	0.792245i	$0.708912\pi$
$572$	47.8241	1.99963
$573$	41.0384	1.71440
$574$	−59.7790	−2.49513
$575$	9.94797	0.414859
$576$	111.494	4.64560
$577$	−41.1313	−1.71232	−0.856160	−	0.516711i	$-0.827156\pi$
$577$	−41.1313	−1.71232	−0.856160	+	0.516711i	$0.827156\pi$
$578$	−71.7366	−2.98385
$579$	0.535542	0.0222564
$580$	−4.25986	−0.176881
$581$	2.83851	0.117761
$582$	47.4577	1.96718
$583$	−56.7445	−2.35012
$584$	−81.7360	−3.38226
$585$	2.08629	0.0862575
$586$	−81.8295	−3.38035
$587$	32.5529	1.34360	0.671801	−	0.740732i	$-0.265521\pi$
$587$	32.5529	1.34360	0.671801	+	0.740732i	$0.265521\pi$
$588$	10.3178	0.425499
$589$	−32.2543	−1.32902
$590$	3.76137	0.154853
$591$	−38.7461	−1.59380
$592$	27.9020	1.14676
$593$	−31.4949	−1.29334	−0.646670	−	0.762770i	$-0.723839\pi$
$593$	−31.4949	−1.29334	−0.646670	+	0.762770i	$0.723839\pi$
$594$	93.8606	3.85115
$595$	3.65833	0.149977
$596$	4.55761	0.186687
$597$	19.9616	0.816972
$598$	−10.2540	−0.419318
$599$	6.47023	0.264367	0.132183	−	0.991225i	$-0.457801\pi$
$599$	6.47023	0.264367	0.132183	+	0.991225i	$0.457801\pi$
$600$	124.973	5.10202
$601$	15.9954	0.652467	0.326234	−	0.945289i	$-0.394220\pi$
$601$	15.9954	0.652467	0.326234	+	0.945289i	$0.394220\pi$
$602$	1.49315	0.0608564
$603$	−40.3143	−1.64173
$604$	122.174	4.97119
$605$	−2.43493	−0.0989938
$606$	−128.875	−5.23519
$607$	−19.0797	−0.774423	−0.387211	−	0.921991i	$-0.626562\pi$
$607$	−19.0797	−0.774423	−0.387211	+	0.921991i	$0.626562\pi$
$608$	−98.9902	−4.01458
$609$	−33.0014	−1.33728
$610$	−6.25899	−0.253419
$611$	−5.26038	−0.212812
$612$	189.381	7.65527
$613$	17.0578	0.688960	0.344480	−	0.938794i	$-0.388055\pi$
$613$	17.0578	0.688960	0.344480	+	0.938794i	$0.388055\pi$
$614$	−26.1916	−1.05701
$615$	4.67230	0.188405
$616$	−115.396	−4.64945
$617$	−32.1552	−1.29452	−0.647260	−	0.762269i	$-0.724085\pi$
$617$	−32.1552	−1.29452	−0.647260	+	0.762269i	$0.724085\pi$
$618$	42.8216	1.72254
$619$	21.0238	0.845018	0.422509	−	0.906359i	$-0.361149\pi$
$619$	21.0238	0.845018	0.422509	+	0.906359i	$0.361149\pi$
$620$	5.80161	0.232998
$621$	−14.5489	−0.583827
$622$	−53.0053	−2.12532
$623$	40.0135	1.60311
$624$	−70.9487	−2.84022
$625$	24.4033	0.976133
$626$	−3.37424	−0.134862
$627$	−81.3027	−3.24692
$628$	−122.876	−4.90328
$629$	14.4147	0.574752
$630$	−8.16228	−0.325193
$631$	9.99235	0.397789	0.198895	−	0.980021i	$-0.436265\pi$
$631$	9.99235	0.397789	0.198895	+	0.980021i	$0.436265\pi$
$632$	−137.815	−5.48198
$633$	−54.9728	−2.18497
$634$	−49.5607	−1.96831
$635$	1.94396	0.0771439
$636$	179.161	7.10422
$637$	−1.29128	−0.0511625
$638$	52.8862	2.09379
$639$	31.5704	1.24891
$640$	4.07368	0.161026
$641$	−18.0052	−0.711164	−0.355582	−	0.934645i	$-0.615717\pi$
$641$	−18.0052	−0.711164	−0.355582	+	0.934645i	$0.615717\pi$
$642$	−144.063	−5.68573
$643$	30.7062	1.21093	0.605467	−	0.795871i	$-0.292986\pi$
$643$	30.7062	1.21093	0.605467	+	0.795871i	$0.292986\pi$
$644$	29.0021	1.14284
$645$	−0.116704	−0.00459522
$646$	−102.909	−4.04891
$647$	39.8503	1.56668	0.783338	−	0.621596i	$-0.213516\pi$
$647$	39.8503	1.56668	0.783338	+	0.621596i	$0.213516\pi$
$648$	−40.3611	−1.58553
$649$	−33.7593	−1.32517
$650$	−25.3597	−0.994688
$651$	44.9455	1.76155
$652$	0.164955	0.00646015
$653$	16.3867	0.641261	0.320630	−	0.947204i	$-0.396105\pi$
$653$	16.3867	0.641261	0.320630	+	0.947204i	$0.396105\pi$
$654$	−141.573	−5.53593
$655$	−1.82810	−0.0714300
$656$	−102.744	−4.01147
$657$	51.8895	2.02440
$658$	20.5804	0.802307
$659$	9.21386	0.358921	0.179461	−	0.983765i	$-0.442565\pi$
$659$	9.21386	0.358921	0.179461	+	0.983765i	$0.442565\pi$
$660$	14.6240	0.569237
$661$	−29.8934	−1.16272	−0.581359	−	0.813647i	$-0.697479\pi$
$661$	−29.8934	−1.16272	−0.581359	+	0.813647i	$0.697479\pi$
$662$	−85.9532	−3.34067
$663$	−36.6535	−1.42350
$664$	8.85790	0.343753
$665$	3.20648	0.124342
$666$	−32.1613	−1.24623
$667$	−8.19765	−0.317414
$668$	12.3834	0.479129
$669$	58.5126	2.26223
$670$	−3.94038	−0.152230
$671$	56.1760	2.16865
$672$	137.940	5.32115
$673$	−10.7190	−0.413189	−0.206594	−	0.978427i	$-0.566238\pi$
$673$	−10.7190	−0.413189	−0.206594	+	0.978427i	$0.566238\pi$
$674$	50.6860	1.95235
$675$	−35.9815	−1.38493
$676$	−48.9434	−1.88244
$677$	49.8842	1.91721	0.958603	−	0.284744i	$-0.0919087\pi$
$677$	49.8842	1.91721	0.958603	+	0.284744i	$0.0919087\pi$
$678$	−18.8324	−0.723254
$679$	16.7987	0.644677
$680$	11.4163	0.437793
$681$	−41.7043	−1.59811
$682$	−72.0271	−2.75806
$683$	−0.147581	−0.00564701	−0.00282351	−	0.999996i	$-0.500899\pi$
$683$	−0.147581	−0.00564701	−0.00282351	+	0.999996i	$0.500899\pi$
$684$	165.990	6.34678
$685$	−0.438261	−0.0167451
$686$	−47.0630	−1.79687
$687$	−54.4913	−2.07897
$688$	2.56632	0.0978402
$689$	−22.4223	−0.854220
$690$	−3.13554	−0.119368
$691$	24.9102	0.947630	0.473815	−	0.880624i	$-0.342877\pi$
$691$	24.9102	0.947630	0.473815	+	0.880624i	$0.342877\pi$
$692$	52.8592	2.00941
$693$	73.2585	2.78286
$694$	−0.603266	−0.0228997
$695$	2.33485	0.0885659
$696$	−102.985	−3.90362
$697$	−53.0795	−2.01053
$698$	34.2728	1.29725
$699$	7.38227	0.279223
$700$	71.7265	2.71101
$701$	22.6338	0.854866	0.427433	−	0.904047i	$-0.359418\pi$
$701$	22.6338	0.854866	0.427433	+	0.904047i	$0.359418\pi$
$702$	37.0885	1.39982
$703$	12.6343	0.476512
$704$	−97.8089	−3.68631
$705$	−1.60855	−0.0605816
$706$	−56.0530	−2.10958
$707$	−45.6183	−1.71565
$708$	106.589	4.00587
$709$	−10.3071	−0.387090	−0.193545	−	0.981091i	$-0.561999\pi$
$709$	−10.3071	−0.387090	−0.193545	+	0.981091i	$0.561999\pi$
$710$	3.08574	0.115806
$711$	87.4907	3.28116
$712$	124.867	4.67958
$713$	11.1646	0.418117
$714$	143.401	5.36665
$715$	−1.83021	−0.0684458
$716$	30.7082	1.14762
$717$	9.24176	0.345140
$718$	−27.0229	−1.00849
$719$	23.6012	0.880175	0.440087	−	0.897955i	$-0.354947\pi$
$719$	23.6012	0.880175	0.440087	+	0.897955i	$0.354947\pi$
$720$	−14.0287	−0.522820
$721$	15.1577	0.564503
$722$	−39.1507	−1.45704
$723$	81.4593	3.02950
$724$	98.4081	3.65731
$725$	−20.2740	−0.752956
$726$	−95.4453	−3.54231
$727$	7.41006	0.274824	0.137412	−	0.990514i	$-0.456122\pi$
$727$	7.41006	0.274824	0.137412	+	0.990514i	$0.456122\pi$
$728$	−45.5982	−1.68998
$729$	−37.7865	−1.39950
$730$	5.07175	0.187714
$731$	1.32581	0.0490370
$732$	−177.367	−6.55567
$733$	30.6034	1.13036	0.565182	−	0.824966i	$-0.308806\pi$
$733$	30.6034	1.13036	0.565182	+	0.824966i	$0.308806\pi$
$734$	18.2241	0.672663
$735$	−0.394857	−0.0145645
$736$	34.2647	1.26301
$737$	35.3659	1.30272
$738$	118.428	4.35940
$739$	22.2896	0.819937	0.409968	−	0.912100i	$-0.365540\pi$
$739$	22.2896	0.819937	0.409968	+	0.912100i	$0.365540\pi$
$740$	−2.27254	−0.0835403
$741$	−32.1263	−1.18019
$742$	87.7235	3.22043
$743$	−2.04677	−0.0750886	−0.0375443	−	0.999295i	$-0.511954\pi$
$743$	−2.04677	−0.0750886	−0.0375443	+	0.999295i	$0.511954\pi$
$744$	140.257	5.14209
$745$	−0.174418	−0.00639018
$746$	−26.0375	−0.953300
$747$	−5.62337	−0.205748
$748$	−166.135	−6.07450
$749$	−50.9946	−1.86330
$750$	−15.5717	−0.568596
$751$	38.4517	1.40312	0.701561	−	0.712609i	$-0.252487\pi$
$751$	38.4517	1.40312	0.701561	+	0.712609i	$0.252487\pi$
$752$	35.3721	1.28989
$753$	−43.4070	−1.58184
$754$	20.8977	0.761049
$755$	−4.67554	−0.170160
$756$	−104.900	−3.81517
$757$	−38.4244	−1.39656	−0.698279	−	0.715825i	$-0.746051\pi$
$757$	−38.4244	−1.39656	−0.698279	+	0.715825i	$0.746051\pi$
$758$	81.4011	2.95662
$759$	28.1423	1.02150
$760$	10.0062	0.362963
$761$	−41.3532	−1.49905	−0.749527	−	0.661974i	$-0.769719\pi$
$761$	−41.3532	−1.49905	−0.749527	+	0.661974i	$0.769719\pi$
$762$	76.2004	2.76045
$763$	−50.1129	−1.81421
$764$	73.5008	2.65917
$765$	−7.24752	−0.262035
$766$	−40.5959	−1.46679
$767$	−13.3398	−0.481672
$768$	41.3280	1.49130
$769$	−32.7620	−1.18143	−0.590714	−	0.806881i	$-0.701154\pi$
$769$	−32.7620	−1.18143	−0.590714	+	0.806881i	$0.701154\pi$
$770$	7.16039	0.258043
$771$	81.3854	2.93102
$772$	0.959170	0.0345213
$773$	−24.1175	−0.867447	−0.433724	−	0.901046i	$-0.642801\pi$
$773$	−24.1175	−0.867447	−0.433724	+	0.901046i	$0.642801\pi$
$774$	−2.95808	−0.106326
$775$	27.6116	0.991839
$776$	52.4224	1.88186
$777$	−17.6055	−0.631595
$778$	−31.6990	−1.13647
$779$	−46.5235	−1.66688
$780$	5.77858	0.206906
$781$	−27.6953	−0.991015
$782$	35.6212	1.27381
$783$	29.6507	1.05963
$784$	8.68291	0.310104
$785$	4.70240	0.167836
$786$	−71.6588	−2.55599
$787$	38.4753	1.37150	0.685748	−	0.727839i	$-0.259475\pi$
$787$	38.4753	1.37150	0.685748	+	0.727839i	$0.259475\pi$
$788$	−69.3952	−2.47210
$789$	−15.3238	−0.545541
$790$	8.55146	0.304247
$791$	−6.66617	−0.237022
$792$	228.612	8.12337
$793$	22.1977	0.788262
$794$	0.493114	0.0174999
$795$	−6.85643	−0.243173
$796$	35.7517	1.26718
$797$	38.0428	1.34755	0.673773	−	0.738939i	$-0.264673\pi$
$797$	38.0428	1.34755	0.673773	+	0.738939i	$0.264673\pi$
$798$	125.689	4.44934
$799$	18.2739	0.646485
$800$	84.7415	2.99607
$801$	−79.2707	−2.80089
$802$	40.8304	1.44177
$803$	−45.5202	−1.60637
$804$	−111.662	−3.93802
$805$	−1.10990	−0.0391188
$806$	−28.4611	−1.00250
$807$	1.85323	0.0652368
$808$	−142.357	−5.00811
$809$	−5.29994	−0.186336	−0.0931681	−	0.995650i	$-0.529699\pi$
$809$	−5.29994	−0.186336	−0.0931681	+	0.995650i	$0.529699\pi$
$810$	2.50442	0.0879965
$811$	22.6397	0.794987	0.397494	−	0.917605i	$-0.369880\pi$
$811$	22.6397	0.794987	0.397494	+	0.917605i	$0.369880\pi$
$812$	−59.1064	−2.07423
$813$	−2.87167	−0.100714
$814$	28.2136	0.988888
$815$	−0.00631276	−0.000221126 0
$816$	246.467	8.62808
$817$	1.16206	0.0406552
$818$	41.7321	1.45913
$819$	28.9477	1.01151
$820$	8.36821	0.292231
$821$	−7.43684	−0.259547	−0.129774	−	0.991544i	$-0.541425\pi$
$821$	−7.43684	−0.259547	−0.129774	+	0.991544i	$0.541425\pi$
$822$	−17.1791	−0.599191
$823$	−12.3351	−0.429974	−0.214987	−	0.976617i	$-0.568971\pi$
$823$	−12.3351	−0.429974	−0.214987	+	0.976617i	$0.568971\pi$
$824$	47.3014	1.64782
$825$	69.6000	2.42316
$826$	52.1898	1.81591
$827$	−30.3758	−1.05627	−0.528136	−	0.849160i	$-0.677109\pi$
$827$	−30.3758	−1.05627	−0.528136	+	0.849160i	$0.677109\pi$
$828$	−57.4561	−1.99674
$829$	0.786811	0.0273271	0.0136635	−	0.999907i	$-0.495651\pi$
$829$	0.786811	0.0273271	0.0136635	+	0.999907i	$0.495651\pi$
$830$	−0.549636	−0.0190781
$831$	57.1291	1.98179
$832$	−38.6486	−1.33990
$833$	4.48576	0.155423
$834$	91.5225	3.16916
$835$	−0.473908	−0.0164003
$836$	−145.615	−5.03621
$837$	−40.3820	−1.39581
$838$	−33.5189	−1.15789
$839$	−1.43958	−0.0496998	−0.0248499	−	0.999691i	$-0.507911\pi$
$839$	−1.43958	−0.0496998	−0.0248499	+	0.999691i	$0.507911\pi$
$840$	−13.9433	−0.481091
$841$	−12.2932	−0.423903
$842$	−19.7076	−0.679170
$843$	−18.0839	−0.622844
$844$	−98.4578	−3.38906
$845$	1.87304	0.0644345
$846$	−40.7718	−1.40176
$847$	−33.7851	−1.16087
$848$	150.773	5.17756
$849$	60.9138	2.09056
$850$	88.0964	3.02168
$851$	−4.37327	−0.149914
$852$	87.4434	2.99576
$853$	10.8068	0.370018	0.185009	−	0.982737i	$-0.440769\pi$
$853$	10.8068	0.370018	0.185009	+	0.982737i	$0.440769\pi$
$854$	−86.8448	−2.97177
$855$	−6.35236	−0.217246
$856$	−159.135	−5.43911
$857$	21.5990	0.737808	0.368904	−	0.929467i	$-0.379733\pi$
$857$	21.5990	0.737808	0.368904	+	0.929467i	$0.379733\pi$
$858$	−71.7412	−2.44921
$859$	11.4973	0.392282	0.196141	−	0.980576i	$-0.437159\pi$
$859$	11.4973	0.392282	0.196141	+	0.980576i	$0.437159\pi$
$860$	−0.209020	−0.00712753
$861$	64.8291	2.20937
$862$	−28.6644	−0.976312
$863$	−44.7377	−1.52289	−0.761444	−	0.648231i	$-0.775509\pi$
$863$	−44.7377	−1.52289	−0.761444	+	0.648231i	$0.775509\pi$
$864$	−123.934	−4.21634
$865$	−2.02290	−0.0687806
$866$	82.8398	2.81501
$867$	77.7969	2.64212
$868$	80.4985	2.73230
$869$	−76.7515	−2.60362
$870$	6.39024	0.216649
$871$	13.9746	0.473512
$872$	−156.383	−5.29580
$873$	−33.2800	−1.12636
$874$	31.2215	1.05608
$875$	−5.51195	−0.186338
$876$	143.723	4.85594
$877$	−14.2907	−0.482564	−0.241282	−	0.970455i	$-0.577568\pi$
$877$	−14.2907	−0.482564	−0.241282	+	0.970455i	$0.577568\pi$
$878$	92.2138	3.11207
$879$	88.7425	2.99321
$880$	12.3068	0.414861
$881$	−31.9299	−1.07574	−0.537872	−	0.843026i	$-0.680772\pi$
$881$	−31.9299	−1.07574	−0.537872	+	0.843026i	$0.680772\pi$
$882$	−10.0084	−0.337000
$883$	−32.1732	−1.08271	−0.541357	−	0.840793i	$-0.682089\pi$
$883$	−32.1732	−1.08271	−0.541357	+	0.840793i	$0.682089\pi$
$884$	−65.6474	−2.20796
$885$	−4.07913	−0.137118
$886$	42.9620	1.44334
$887$	23.7127	0.796193	0.398097	−	0.917343i	$-0.369671\pi$
$887$	23.7127	0.796193	0.398097	+	0.917343i	$0.369671\pi$
$888$	−54.9401	−1.84367
$889$	26.9729	0.904642
$890$	−7.74803	−0.259714
$891$	−22.4778	−0.753036
$892$	104.798	3.50888
$893$	16.0168	0.535983
$894$	−6.83691	−0.228660
$895$	−1.17519	−0.0392823
$896$	56.5231	1.88830
$897$	11.1203	0.371295
$898$	12.8761	0.429680
$899$	−22.7534	−0.758869
$900$	−142.097	−4.73657
$901$	77.8922	2.59497
$902$	−103.892	−3.45921
$903$	−1.61929	−0.0538867
$904$	−20.8025	−0.691882
$905$	−3.76603	−0.125187
$906$	−183.274	−6.08887
$907$	22.3031	0.740564	0.370282	−	0.928919i	$-0.379261\pi$
$907$	22.3031	0.740564	0.370282	+	0.928919i	$0.379261\pi$
$908$	−74.6935	−2.47879
$909$	90.3745	2.99753
$910$	2.82939	0.0937933
$911$	−13.1150	−0.434521	−0.217260	−	0.976114i	$-0.569712\pi$
$911$	−13.1150	−0.434521	−0.217260	+	0.976114i	$0.569712\pi$
$912$	216.025	7.15331
$913$	4.93312	0.163262
$914$	−97.1709	−3.21413
$915$	6.78775	0.224396
$916$	−97.5953	−3.22464
$917$	−25.3653	−0.837637
$918$	−128.841	−4.25239
$919$	−8.29184	−0.273523	−0.136761	−	0.990604i	$-0.543669\pi$
$919$	−8.29184	−0.273523	−0.136761	+	0.990604i	$0.543669\pi$
$920$	−3.46357	−0.114191
$921$	28.4043	0.935953
$922$	109.621	3.61018
$923$	−10.9436	−0.360214
$924$	202.911	6.67527
$925$	−10.8157	−0.355619
$926$	−39.5192	−1.29868
$927$	−30.0289	−0.986280
$928$	−69.8315	−2.29233
$929$	25.6245	0.840711	0.420356	−	0.907359i	$-0.361905\pi$
$929$	25.6245	0.840711	0.420356	+	0.907359i	$0.361905\pi$
$930$	−8.70303	−0.285384
$931$	3.93171	0.128857
$932$	13.2218	0.433096
$933$	57.4832	1.88191
$934$	110.574	3.61810
$935$	6.35792	0.207926
$936$	90.3347	2.95268
$937$	15.0035	0.490142	0.245071	−	0.969505i	$-0.421189\pi$
$937$	15.0035	0.490142	0.245071	+	0.969505i	$0.421189\pi$
$938$	−54.6735	−1.78515
$939$	3.65929	0.119416
$940$	−2.88096	−0.0939666
$941$	15.2554	0.497310	0.248655	−	0.968592i	$-0.420011\pi$
$941$	15.2554	0.497310	0.248655	+	0.968592i	$0.420011\pi$
$942$	184.327	6.00569
$943$	16.1038	0.524410
$944$	89.7000	2.91949
$945$	4.01447	0.130591
$946$	2.59499	0.0843704
$947$	−18.9088	−0.614453	−0.307226	−	0.951636i	$-0.599401\pi$
$947$	−18.9088	−0.614453	−0.307226	+	0.951636i	$0.599401\pi$
$948$	242.331	7.87053
$949$	−17.9871	−0.583885
$950$	77.2153	2.50520
$951$	53.7475	1.74288
$952$	158.403	5.13387
$953$	18.8302	0.609969	0.304985	−	0.952357i	$-0.401349\pi$
$953$	18.8302	0.609969	0.304985	+	0.952357i	$0.401349\pi$
$954$	−173.789	−5.62663
$955$	−2.81284	−0.0910215
$956$	16.5522	0.535338
$957$	−57.3540	−1.85399
$958$	16.1915	0.523124
$959$	−6.08096	−0.196364
$960$	−11.8182	−0.381432
$961$	−0.0115178	−0.000371543 0
$962$	11.1485	0.359441
$963$	101.025	3.25550
$964$	145.896	4.69899
$965$	−0.0367070	−0.00118164
$966$	−43.5063	−1.39979
$967$	50.3023	1.61761	0.808807	−	0.588075i	$-0.200114\pi$
$967$	50.3023	1.61761	0.808807	+	0.588075i	$0.200114\pi$
$968$	−105.430	−3.38866
$969$	111.603	3.58520
$970$	−3.25283	−0.104442
$971$	−5.64534	−0.181168	−0.0905838	−	0.995889i	$-0.528873\pi$
$971$	−5.64534	−0.181168	−0.0905838	+	0.995889i	$0.528873\pi$
$972$	−42.5979	−1.36633
$973$	32.3965	1.03858
$974$	−59.5932	−1.90949
$975$	27.5020	0.880770
$976$	−149.263	−4.77778
$977$	−15.1978	−0.486222	−0.243111	−	0.969998i	$-0.578168\pi$
$977$	−15.1978	−0.486222	−0.243111	+	0.969998i	$0.578168\pi$
$978$	−0.247450	−0.00791259
$979$	69.5405	2.22252
$980$	−0.707200	−0.0225907
$981$	99.2787	3.16973
$982$	6.73373	0.214882
$983$	36.4666	1.16310	0.581552	−	0.813510i	$-0.302446\pi$
$983$	36.4666	1.16310	0.581552	+	0.813510i	$0.302446\pi$
$984$	202.307	6.44930
$985$	2.65572	0.0846184
$986$	−72.5961	−2.31193
$987$	−22.3190	−0.710422
$988$	−57.5391	−1.83056
$989$	−0.402237	−0.0127904
$990$	−14.1854	−0.450843
$991$	−26.8798	−0.853866	−0.426933	−	0.904283i	$-0.640406\pi$
$991$	−26.8798	−0.853866	−0.426933	+	0.904283i	$0.640406\pi$
$992$	95.1053	3.01960
$993$	93.2145	2.95807
$994$	42.8152	1.35802
$995$	−1.36820	−0.0433749
$996$	−15.5755	−0.493530
$997$	1.23346	0.0390640	0.0195320	−	0.999809i	$-0.493782\pi$
$997$	1.23346	0.0390640	0.0195320	+	0.999809i	$0.493782\pi$
$998$	1.91225	0.0605311
$999$	15.8180	0.500459

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8017.2.a.b.1.7	✓	340

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8017.2.a.b.1.7	✓	340	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.68673 q^{2} +2.91370 q^{3} +5.21852 q^{4} -0.199710 q^{5} -7.82834 q^{6} -2.77102 q^{7} -8.64730 q^{8} +5.48967 q^{9} +O(q^{10})\)	\(q-2.68673 q^{2} +2.91370 q^{3} +5.21852 q^{4} -0.199710 q^{5} -7.82834 q^{6} -2.77102 q^{7} -8.64730 q^{8} +5.48967 q^{9} +0.536568 q^{10} -4.81584 q^{11} +15.2052 q^{12} -1.90295 q^{13} +7.44499 q^{14} -0.581897 q^{15} +12.7959 q^{16} +6.61062 q^{17} -14.7493 q^{18} +5.79412 q^{19} -1.04219 q^{20} -8.07394 q^{21} +12.9389 q^{22} -2.00559 q^{23} -25.1957 q^{24} -4.96012 q^{25} +5.11272 q^{26} +7.25417 q^{27} -14.4606 q^{28} +4.08740 q^{29} +1.56340 q^{30} -5.56673 q^{31} -17.0846 q^{32} -14.0319 q^{33} -17.7610 q^{34} +0.553402 q^{35} +28.6480 q^{36} +2.18054 q^{37} -15.5672 q^{38} -5.54464 q^{39} +1.72696 q^{40} -8.02943 q^{41} +21.6925 q^{42} +0.200558 q^{43} -25.1315 q^{44} -1.09635 q^{45} +5.38849 q^{46} +2.76433 q^{47} +37.2835 q^{48} +0.678569 q^{49} +13.3265 q^{50} +19.2614 q^{51} -9.93059 q^{52} +11.7829 q^{53} -19.4900 q^{54} +0.961773 q^{55} +23.9619 q^{56} +16.8824 q^{57} -10.9817 q^{58} +7.01005 q^{59} -3.03664 q^{60} -11.6649 q^{61} +14.9563 q^{62} -15.2120 q^{63} +20.3099 q^{64} +0.380039 q^{65} +37.7000 q^{66} -7.34367 q^{67} +34.4977 q^{68} -5.84370 q^{69} -1.48684 q^{70} +5.75088 q^{71} -47.4708 q^{72} +9.45220 q^{73} -5.85851 q^{74} -14.4523 q^{75} +30.2368 q^{76} +13.3448 q^{77} +14.8969 q^{78} +15.9373 q^{79} -2.55548 q^{80} +4.66748 q^{81} +21.5729 q^{82} -1.02435 q^{83} -42.1340 q^{84} -1.32021 q^{85} -0.538845 q^{86} +11.9095 q^{87} +41.6440 q^{88} -14.4400 q^{89} +2.94558 q^{90} +5.27312 q^{91} -10.4662 q^{92} -16.2198 q^{93} -7.42700 q^{94} -1.15715 q^{95} -49.7794 q^{96} -6.06229 q^{97} -1.82313 q^{98} -26.4374 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9}+O(q^{10}) \) 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9	\( 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9} + 36 q^{10} + 70 q^{11} + 92 q^{12} + 45 q^{13} + 44 q^{14} + 71 q^{15} + 362 q^{16} + 162 q^{17} + 41 q^{18} + 49 q^{19} + 147 q^{20} + 41 q^{21} + 32 q^{22} + 244 q^{23} + 85 q^{24} + 355 q^{25} + 83 q^{26} + 155 q^{27} + 129 q^{28} + 91 q^{29} + 51 q^{30} + 65 q^{31} + 113 q^{32} + 73 q^{33} + 26 q^{34} + 200 q^{35} + 380 q^{36} + 28 q^{37} + 171 q^{38} + 117 q^{39} + 95 q^{40} + 115 q^{41} + 42 q^{42} + 98 q^{43} + 139 q^{44} + 127 q^{45} + 29 q^{46} + 312 q^{47} + 168 q^{48} + 365 q^{49} + 64 q^{50} + 72 q^{51} + 100 q^{52} + 154 q^{53} + 89 q^{54} + 161 q^{55} + 89 q^{56} + 82 q^{57} + 29 q^{58} + 149 q^{59} + 93 q^{60} + 70 q^{61} + 257 q^{62} + 376 q^{63} + 346 q^{64} + 125 q^{65} + 48 q^{66} + 65 q^{67} + 464 q^{68} + 58 q^{69} - 54 q^{70} + 216 q^{71} + 90 q^{72} + 93 q^{73} + 147 q^{74} + 162 q^{75} + 64 q^{76} + 190 q^{77} + 12 q^{78} + 139 q^{79} + 274 q^{80} + 376 q^{81} + 59 q^{82} + 402 q^{83} + 10 q^{84} + 32 q^{85} + 53 q^{86} + 364 q^{87} + 42 q^{88} + 114 q^{89} + 126 q^{90} + 43 q^{91} + 422 q^{92} + 47 q^{93} + 2 q^{94} + 347 q^{95} + 146 q^{96} + 47 q^{97} + 96 q^{98} + 129 q^{99}+O(q^{100}) \) 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9 + 36 * q^10 + 70 * q^11 + 92 * q^12 + 45 * q^13 + 44 * q^14 + 71 * q^15 + 362 * q^16 + 162 * q^17 + 41 * q^18 + 49 * q^19 + 147 * q^20 + 41 * q^21 + 32 * q^22 + 244 * q^23 + 85 * q^24 + 355 * q^25 + 83 * q^26 + 155 * q^27 + 129 * q^28 + 91 * q^29 + 51 * q^30 + 65 * q^31 + 113 * q^32 + 73 * q^33 + 26 * q^34 + 200 * q^35 + 380 * q^36 + 28 * q^37 + 171 * q^38 + 117 * q^39 + 95 * q^40 + 115 * q^41 + 42 * q^42 + 98 * q^43 + 139 * q^44 + 127 * q^45 + 29 * q^46 + 312 * q^47 + 168 * q^48 + 365 * q^49 + 64 * q^50 + 72 * q^51 + 100 * q^52 + 154 * q^53 + 89 * q^54 + 161 * q^55 + 89 * q^56 + 82 * q^57 + 29 * q^58 + 149 * q^59 + 93 * q^60 + 70 * q^61 + 257 * q^62 + 376 * q^63 + 346 * q^64 + 125 * q^65 + 48 * q^66 + 65 * q^67 + 464 * q^68 + 58 * q^69 - 54 * q^70 + 216 * q^71 + 90 * q^72 + 93 * q^73 + 147 * q^74 + 162 * q^75 + 64 * q^76 + 190 * q^77 + 12 * q^78 + 139 * q^79 + 274 * q^80 + 376 * q^81 + 59 * q^82 + 402 * q^83 + 10 * q^84 + 32 * q^85 + 53 * q^86 + 364 * q^87 + 42 * q^88 + 114 * q^89 + 126 * q^90 + 43 * q^91 + 422 * q^92 + 47 * q^93 + 2 * q^94 + 347 * q^95 + 146 * q^96 + 47 * q^97 + 96 * q^98 + 129 * q^99

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